Problem 65 - Chemistry: An Atoms-Focused Approach

Question

A brand new silver U.S. dollar weighs 0.934 oz. Express this mass in grams and kilograms. \((1 \mathrm{oz}=28.35 \mathrm{g} .)\)

Step-by-Step Solution

Answer

Answer: The mass of a new silver U.S. dollar is approximately 26.47 g and 0.02647 kg.

Step 1: Identify the given mass

The mass of a new silver U.S. dollar in ounces is given: \(0.934 \, \mathrm{oz}\).

Step 2: Convert the mass to grams

We are given the conversion factor: \(1 \, \mathrm{oz} = 28.35 \, \mathrm{g}\). To convert the mass of the silver dollar to grams, we'll multiply the given mass in ounces by this conversion factor: \(0.934 \, \mathrm{oz} \times \frac{28.35 \, \mathrm{g}}{1 \, \mathrm{oz}} = 26.4689 \, \mathrm{g}\) So, the mass of the silver dollar in grams is approximately 26.47 g.

Step 3: Convert the mass to kilograms

Since we know that there are \(1000\,\mathrm{g}\) in a kilogram, we can convert the mass in grams to kilograms by dividing by 1000: \(26.4689 \, \mathrm{g} \times \frac{1 \, \mathrm{kg}}{1000 \, \mathrm{g}} = 0.0264689 \, \mathrm{kg}\). So, the mass of the silver dollar in kilograms is approximately 0.02647 kg.

Key Concepts

Converting Ounces to Grams

When converting from ounces to grams, it's essential to know the conversion factor that links these two units. An ounce (oz) is a unit of weight used mainly in the United States, while the gram (g) is a metric unit, favored in many other countries. The conversion factor is:

• 1 ounce = 28.35 grams

To convert ounces to grams, we multiply the number of ounces by 28.35. For example, if you have a silver dollar that weighs 0.934 oz, the conversion to grams is straightforward:
Use the formula:
0.934 oz × 28.35 g/oz = 26.4689 g
Therefore, 0.934 ounces is approximately 26.47 grams when rounded to two decimal places. This is a handy conversion for anybody dealing with recipes, postage, or even conducting scientific experiments. Remember, multiplying the ounces by the conversion factor gives you the mass in grams directly.

Converting Grams to Kilograms

Once you have the mass in grams, converting it to kilograms is the next step. The kilogram is the base unit of mass in the metric system. Here's the essential conversion information:

• 1 kilogram = 1000 grams

To convert grams to kilograms, divide the number of grams by 1000. This is because there are 1000 grams in a single kilogram. For example, with the weight of the silver dollar:
26.4689 g ÷ 1000 g/kg = 0.0264689 kg
The weight in kilograms is thus approximately 0.02647 kg. Dividing by 1000 simplifies the number and expresses it in a larger unit, convenient for scientific calculations and when communicating large quantities of mass.

The Importance of Unit Conversion

Unit conversion is a vital skill in chemistry, physics, engineering, and everyday life. You encounter different measurement systems across various contexts, and being able to convert between them ensures accuracy and understanding.
Some important reasons for mastering unit conversion include:

• Consistency in scientific research and global communication.
• Accuracy in cooking and baking, where even small differences matter.
• Understanding product weights and volumes when shopping internationally.

Different regions use different systems, like the imperial system in the U.S. and the metric system worldwide. Knowing how to switch between ounces, grams, and kilograms means you can work seamlessly, no matter the unit.
Start practicing conversions in real-life scenarios to become more familiar. Whether it's converting a grocery list, modifying a recipe, or even assessing a precious coin collection, the more you practice, the better you'll become. This ensures that you’ll be prepared for any conversion need you might encounter.